Research Article

On power sums of Fourier coefficients of cusp forms

Published in: Quaestiones Mathematicae
Volume 49 , issue 2 , 2026 , pages: 231–248

DOI: 10.2989/16073606.2025.2576678

Author(s): Huafeng Liu Shandong Normal University, China , Jingyang Lü Shandong Normal University, China

Keywords: 11F30 , 11F11 , 11F66 , Fourier coefficient , cusp form , power sum

Abstract

We denote by λ _f (n) the n-th normalized Fourier coefficient of primitive holomorphic cusp form of even integral weight k ≥ 2 for the full modular group SL(2,). In this paper, we prove asymptotic formulae for l-th power sums of two types related to the Fourier coefficient λ _f (n), which refines previous results.

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